Answered

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The heights of male students are normally distributed with a mean of 158 cm and a

standard deviation of 5 cm.


Find the percentage of male students who are between 145 cm and 170 cm.


Round your

answers to the nearest hundredths.

Sagot :

JeanaShupp

Answer: The percentage of male students who are between 145 cm and 170 cm = 98.71%

Step-by-step explanation:

Let x denotes the height of male students.

As per given,

[tex]\mu=158,\sigma=5[/tex]

The probability of male students who are between 145 cm and 170 cm

= [tex]P(145<X<170)[/tex]

[tex]=P(\dfrac{145-158}{5}<\dfrac{X-\mu}{\sigma}<\dfrac{170-158}{5})\\\\=P(-2.6<Z<2.4)\\\\=P(Z<2.4)-P(Z<-2.6)\\\\=P(Z<2.4)-(1-P(2.6))\\\\=0.9918-(1-0.9953)\\\\= $0.9871[/tex]

Hence, the percentage of male students who are between 145 cm and 170 cm = 98.71%

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